Density and irregularity dependence of partial recovery codes

Classical linear block codes, such as Reed-Solomon (RS)-based codes, fail to recover any lost message symbols when the total losses exceed the redundant symbols. Under such adverse channel conditions, source and/or channel rate adaptation to incorporate additional redundancy might not be a viable option. In this paper, we explore a novel method of code adaptation which alters the degree distribution in order to achieve partial recovery of information when complete recovery is not possible. In particular, we change the degree distribution by adjusting the density and irregularity of the code. First, we illustrate that, while maintaining a constant rate, a partial recovery code can be optimized by density modification. Then, we focus on the Partial Reed-Solomon (PRS) codes, which are a family of RS-based codes that are capable of achieving different levels of partial recovery by adjustment to their order. We analyze the dependence of erasure recovery of these codes on density and regularity for a given number of losses. Finally, we present results and analysis which demonstrate that, for a given number of erasures, the PRS codes of order-1 render optimal (erasure-recovery) performance.